Beyond the Classical Copula : Artificial Intelligence Methods and Neural Copulas for Modeling Reserve Dependence in Non-Life Insurance

Hajar Ettaya, Tarek Zari

Traditional copulas, although they have revolutionized dependence modeling by separating marginal structures from joint structures, present significant limitations in non-life insurance, where technical reserves (IBNR and RBNS) across multiple lines of business exhibit complex, asymmetric dependencies that intensify in the tail during extreme events (natural catastrophes, claims inflation, regulatory shocks). Through a critical literature review, this paper examines to what extent machine learning models and neural copulas can overcome these limitations for modeling reserve dependence. We detail the mathematical foundations and learning mechanisms of the main neural architectures applied to copulas IGNIS parametric estimation networks, GARCH-RBM models, deep neural copulas, copula-nested spectral kernel networks as well as reserving-specific neural approaches such as the neural Chain-Ladder, DeepTriangle, and its multi-line extension. A structured analytical comparison, based exclusively on results reported in the literature and explicitly referenced, highlights the trade-offs between expressive flexibility, interpretability, theoretical guarantees, and computational cost. We conclude that hybridization between actuarial rigor and the representational power of neural networks constitutes the most promising path for modeling complex dependencies in non-life reserving, subject to rigorous empirical validation on real data.